Computer Networks 54 (2010) Contents lists available at ScienceDirect. Computer Networks. journal homepage:

Computer Networks 54 (21) 3264 3279 Contents lists available at ScienceDirect Computer Networks journal homepage: www.elsevier.com/locate/comnet Topology-aware wavelength partitioning for DWDM OBS networks: A novel approach for absolute QoS provisioning Abdeltouab Belbekkouche a, Abdelhakim Hafid a, *, Mariam Tagmouti b, Michel Gendreau b a Network Research Laboratory, University of Montreal, Montreal, Canada b CIRRELT, University of Montreal, Montreal, Canada article info abstract Article history: Received 8 February 21 Received in revised form 14 May 21 Accepted 28 June 21 Available online 1 July 21 Responsible Editor: J. Sole-Pareta Keywords: Optical Burst Switching (OBS) Quality of Service (QoS) Admission control Linear programming Tabu search Wavelength assignment Fairness Dense Wavelength Division Multiplexing (DWDM) Optical Burst Switching (OBS) is a promising switching technology for the next generation all-optical networks. An OBS network without wavelength converters and fiber delay lines can be implemented simply and cost-effectively using the existing technology. However, this kind of networks suffers from a relatively high burst loss probability at the OBS core nodes. To overcome this issue and consolidate OBS networks with QoS provisioning capabilities, we propose a wavelength partitioning approach, called Optimization-based Topology-aware Wavelength Partitioning approach (OTWP). OTWP formulates the wavelength partitioning problem, based on the topology of the network, as an Integer Linear Programming (ILP) model and uses a tabu search algorithm (TS) to resolve large instances efficiently. We use OTWP to develop an absolute QoS differentiation scheme, called Absolute Fair Quality of service Differentiation scheme (AFQD). AFQD is the first absolute QoS provisioning scheme that guarantees loss-free transmission for high priority traffic, inside the OBS network, regardless of its topology. Also, we use OTWP to develop a wavelength assignment scheme, called Best Effort Traffic Wavelength Assignment scheme (BET- WA). BETWA aims to reduce loss probability for best effort traffic. To make AFQD adaptive to non-uniform traffic, we develop a wavelength borrowing protocol, called Wavelength Borrowing Protocol (WBP). Numerical results show the effectiveness of the proposed tabu search algorithm to resolve large instances of the partitioning problem. Also, simulation results, using ns-2, show that: (a) AFQD provides an excellent quality of service differentiation; (b) BETWA substantially decreases the loss probability of best effort traffic to a remarkably low level for the OBS network under study; and (c) WBP makes AFQD adaptive to non-uniform traffic by reducing efficiently blocking probability for high priority traffic. Ó 21 Elsevier B.V. All rights reserved. 1. Introduction Optical Burst Switching [1] is a promising switching technology for the next generation all-optical networks. It is considered as a tradeoff between Optical Circuit Switching (OCS) and Optical Packet Switching (OPS). OCS is easy to implement but suffers from poor * Corresponding author. E-mail addresses: belbekka@iro.umontreal.ca (A. Belbekkouche), ahafid@iro.umontreal.ca (A. Hafid), mariam.tagmouti@cirrelt.ca (M. Tagmouti), michel.gendreau@cirrelt.ca (M. Gendreau). bandwidth utilization and coarse granularity. OPS has a good bandwidth utilization and fine granularity but suffers from complex implementation because of the immaturity of the current technologies, such as optical buffers and ultra fast optical switches [1]. Hence, OBS is a good switching technology to benefit from the potential bandwidth that exists in optical fibers when used with Dense Wavelength Division Multiplexing (DWDM) technology. Indeed, theoretical research on OBS networks has reached the stage of prototypes in research laboratories [2,3] and even commercial products (e.g., EtherBurst optical switch [4]). Hence, OBS networks could play an 1389-1286/$ - see front matter Ó 21 Elsevier B.V. All rights reserved. doi:1.116/j.comnet.21.6.17

A. Belbekkouche et al. / Computer Networks 54 (21) 3264 3279 3265 important role in metropolitan, access and local area optical networks. In OBS networks, data packets with the same destination are aggregated in bursts of variable lengths at the ingress node, this is called Burst Assembly. After burst assembly, a Control Packet (also, called Burst Header Packet) is sent, using a dedicated control wavelength, from source to destination in order to reserve the required resources along a lightpath. This control packet is subject to Optical/Electronic/Optical (O/E/O) transformations at each core node (OBS switch) where it receives an appropriate processing. After a delay, called Offset Time (OT), the corresponding data burst is sent, on one of the data wavelengths, through the same lightpath (all-optically) without any buffering requirement inside the OBS network. Wavelength contention is the main cause of burst losses in OBS networks. A wavelength contention occurs when two or more bursts intend to take the same output fiber, on the same wavelength, at the same time. Hence, a Quality of Service (QoS) scheme for OBS networks has to consider how to deal with wavelength contentions for each class of traffic. In fact, reducing loss probability for the OBS network is performed by reducing the level of wavelength contentions in the network. Moreover, in the context of multi-class traffic, reducing the loss probability of a given class of traffic can be performed by privileging this class in the case of contentions. It is worth noting that the store-and-forward based QoS schemes developed for electronic networks cannot be applied for OBS networks because of the lack of Random Access Memory (RAM) for optical networks. In this paper, we consider absolute QoS provisioning for OBS networks. We propose a novel scheme, called Absolute Fair Quality of service Differentiation scheme (AFQD), which guarantees, for the first time, loss-free transmission for high priority bursts whatever the kind of the OBS network topology. AFQD is based on a wavelength partitioning approach, called Optimization-based Topology-aware Wavelength Partitioning scheme (OTWP), which uses Integer Linear Programming (ILP) to partition data wavelengths among the nodes in the network. Also, AFQD considers fairness among the users (nodes) of the network by allocating the same amount of bandwidth for high priority traffic to each user. Moreover, we propose a wavelength assignment scheme, called Best Effort Traffic Wavelength Assignment scheme (BETWA), which uses the wavelength partitioning approach OTWP to improve the performance of Best Effort traffic in terms of loss probability. To make AFQD adaptive to the case when high priority traffic pattern is non-uniform, we propose a Wavelength Borrowing Protocol (WBP) which aims to exploit non-utilized bandwidth while keeping the capabilities offered by AFQD (e.g., absolute QoS differentiation and fairness). We consider an OBS network without wavelength converters and without Fiber Delay Lines (FDLs). This assumption is relevant since: (a) currently, wavelength conversion devices are complex, expensive, and not technologically mature; and (b) FDLs suffer from the lack of flexibility. Thus, the network under study can be implemented simply and cost-effectively using existing optical networks technology. Furthermore, this assumption allows measuring the performance improvement brought exclusively by our proposed schemes. We adopt Just Enough Time (JET) [1] protocol for resource reservation. The remainder of this paper is organized as follows. In Section 2 we present related work. Section 3 presents a description of the proposed wavelength partitioning approach (OTWP), the exact ILP formulation of the wavelength partitioning problem and the proposed tabu search algorithm. Section 4, presents the proposed absolute QoS differentiation scheme (AFQD) and the proposed wavelength assignment scheme for best effort traffic (BETWA). Section 5 presents the proposed wavelength borrowing protocol (WBP). In Section 6, we present (1) numerical results that show the performance of the proposed tabu search algorithm and the ILP model resolution and (2) simulation results that show the performance of AFQD, BETWA and WBP. Finally, Section 7 concludes the paper. 2. Related work 2.1. Absolute QoS provisioning In the literature, we find two kinds of QoS differentiation schemes for OBS networks: relative QoS differentiation [5,6] and absolute QoS differentiation [7 11]. Whereas absolute QoS guarantees, quantitatively, hard QoS requirements for high priority bursts, relative QoS just guarantees that high priority bursts will be served with higher quality (e.g., smaller loss probability) compared to low priority bursts. Notice that the main QoS parameter inside the OBS network is loss probability since data bursts are switched in the optical domain at each OBS switch without any queuing delay, especially, when Fiber Delay Lines (FDLs) are not used. In [7 11], absolute QoS differentiation schemes are proposed. In [7], the proposed QoS differentiation scheme is based on a dynamic wavelength assignment approach where wavelengths are shared (dynamically) among different classes of traffic. The authors in [8] propose two schemes for absolute QoS provisioning: Early Dropping (ED) and Wavelength Grouping (WG). Early Dropping drops intentionally and probabilistically low priority bursts in order to maintain the level of loss probability of guaranteed bursts. Early dropping increases the loss probability for low priority traffic and the overall burst loss probability compared to the classless case. Wavelength Grouping (WG) provisions wavelengths for the guaranteed traffic and schedules bursts based on this provisioning mechanism. The authors in [9] propose a mechanism that guarantees a maximum loss probability for each guaranteed class of traffic. To do so, each core OBS node has to maintain traffic statistics for each class of traffic; a guaranteed burst can preempt a non-guaranteed burst (i.e., cancel its reservation) proactively according to a given preemption probability. The authors in [1] propose Reserveand-Preempt Scheme (RPS) to improve the bandwidth provisioning of best effort traffic in the context of absolute QoS differentiation. In RPS, a metric, called Distance To Threshold (DTT), measures the difference between each

3266 A. Belbekkouche et al. / Computer Networks 54 (21) 3264 3279 priority guaranteed class loss rate and its pre-set loss rate threshold. Based on the value of DTT and using one of several proposed scenarios, a best effort burst can even preempt a priority guaranteed burst if the DTT of its class is: (a) big enough; and (b) the maximum among other priority guaranteed classes DTTs. The same authors in [11] propose several schemes which integrate RPS and wavelength grouping schemes in order to ensure that the highest priority guaranteed classes can be provided with their respective guaranteed loss rates. We can see that all of the above absolute QoS schemes consider a target value or a threshold for loss probability for high priority traffic. 2.2. Wavelength assignment Despite its key role for data bursts transmission in OBS networks, wavelength assignment has not received much attention in the literature of OBS networks. This is due to the fact that most existing contributions assume that wavelength conversion capability is always present in OBS networks. However, this assumption is simplistic from both technical and economical points of view. Furthermore, this assumption could over-estimate the performance of OBS networks. Indeed, wavelength converters eliminate the wavelength continuity constraint (which stipulates that each data burst should be transmitted on the same wavelength from source to destination); a data burst could change its wavelength at any intermediate OBS node equipped with a wavelength converter. In addition, most of the authors use classical resource reservation policies in wavelength routed networks (e.g., First-Fit, Least Used and Random policies) for wavelength assignment in OBS networks. However, these policies are not adapted to OBS networks [12]. Almost all of the proposed wavelength assignment schemes for OBS networks can be characterized as feedback-based (adaptive) schemes [12 14]. The authors in [13] propose Priority-based Wavelength Assignment (PWA) algorithm. In PWA, each node in the OBS network maintains locally a priority value for each (wavelength, destination node) pair. Priorities are updated using feedbacks received after the transmission of data bursts; if the transmission was successful, priorities would be increased; otherwise, priorities would be decreased. To transmit a data burst, the node searches for a free wavelength in decreasing order of priorities. It is reported in [13] that PWA performs better than Random wavelength assignment policy (in terms of loss probability) under low traffic load; however, it performs only marginally better than Random policy under high traffic load. The authors in [12] propose two variants of PWA, namely, PWA-link and PWA-lambda. In PWA-link, each node associates a priority value to every (wavelength, link) pair (rather than (wavelength, node) pair in PWA) which results in finer granularity at the cost of more information exchange in the network. In PWA-lambda, each node associates a priority value to every wavelength; this makes PWA-lambda simpler and easier to implement but with worse performance compared to both PWA and PWA-link. Indeed, numerical results in [12] show that PWA-link is the best and PWA-lambda is the worst when comparing PWA, PWA-link and PWA-lambda. More recently, the authors in [14] propose another feedback-based wavelength assignment scheme, called Q-learning algorithm for Wavelength Selection (QWS). QWS is different from PWA in that it uses reinforcement algorithm (a Q-learning algorithm) to update priorities. The authors in [12] also propose a nonadaptive wavelength assignment scheme called First-Fit- TE where TE stands for traffic engineering. In First-Fit-TE, nodes are assigned start wavelengths depending on the traffic pattern and the fixed routing paths between nodes in the OBS network. Using First-Fit-TE, each node searches a free wavelength to transmit its data bursts starting from its start wavelength. The aim of First-Fit-TE is to improve the way First-Fit policy assigns a free wavelength. However, First-Fit-TE operation depends strongly on a priori known traffic pattern and (fixed) routing paths; this could limit its use (a) for OBS networks with dynamic (or even unknown) traffic patterns; and (b) when alternative routing is adopted. In this paper, we propose, for the first time, a wavelength assignment scheme (BETWA) which will be used to improve the performance of best effort traffic. BET- WA uses the wavelength partitioning approach (OTWP) that formulates the partitioning problem as an Integer Linear Programming (ILP) model; the objective is to assign a wavelength interval to each node based on the topology of the OBS network which rarely changes (in opposition to traffic patterns and routing paths that change more often). 3. Optimization-based topology-aware wavelength partitioning approach In this Section, we present our wavelength partitioning scheme, called Optimization-based Topology-aware Wavelength Partitioning scheme (OTWP). First, we present a description of OTWP. Then, we present an exact formulation of wavelength partitioning in OTWP as an Integer Linear Programming (ILP) model. Finally, we present a tabu search algorithm to resolve efficiently the proposed ILP model. 3.1. OTWP description The idea of OTWP is to allocate a number of wavelengths (one or more) to each OBS edge node in the network by considering the network topology. To this end, we model the OBS network as a graph G(V,E) where V is the set of nodes (jvj = N) and E is the set of links (jej = M). We suppose that each DWDM fiber link operates with W wavelengths where W is supposed to be bigger than N. If the number of wavelengths in each link is different, we can simply consider the number of wavelengths in the link with the minimum number of wavelengths or we can use a more sophisticated approach where each node is assigned a number of local wavelengths proportional to the number of wavelengths in its outgoing links; however, this is out of the scope of this paper. Also, additional optical fibers could be added to a link to increase its number of wavelengths (bandwidth capacity) if necessary; this ensures the scalability of OTWP. Hence, OTWP allocates a

A. Belbekkouche et al. / Computer Networks 54 (21) 3264 3279 3267 wavelength interval (i.e., a number of wavelengths) of size W/N to each node in the OBS network based on topological constraints, i.e., the closer two nodes to each other (i.e., the smaller the distance between the nodes), the more distant their allocated wavelength intervals from each other (i.e., the larger the distance between the intervals). We note that the size of wavelength intervals, represented by the ratio W/N, may be further increased by capturing edge nodes in the OBS network for which routing paths do not overlap (i.e., do not use any common link); in this case, bursts sent from these nodes will never contend among themselves, and hence, these nodes could use the same wavelength interval. For example, if we have h (two or more) edge nodes for which routing paths do not overlap, wavelength interval size is given by W/(N (h 1)). The problem of increasing wavelength interval size is out of the scope of this paper; hence, in the rest of this paper, we consider that wavelength interval size is fixed to W/N. For a given node i 2 {,...,N 1}, its allocated wavelength interval is denoted by i 2 {,...,N 1}. The first wavelength in the wavelength interval i is computed as follows: ( Stði Þ¼ bi ðw=nþc if ½i ðw=nþ bi ðw=nþc < :5Š; di ðw=nþe otherwise: ð1þ Thus, even if the size of wavelength intervals W/N is not always an integer value, we use floor and ceil functions to determine the start wavelength of each wavelength interval. The distance between two wavelength intervals i and j, denoted by D(i,j ), is calculated as follows: Dði ; j Þ¼ji j j: ð2þ The distance between two nodes i and j in the network, denoted d(i,j), is equal to the number of hops of the shortest path between nodes i and j. Fig. 1 shows an example of the operation of OTWP scheme using a linear topology of 4 nodes and 3 fiber links with 12 wavelengths on each link. We note that all of the nodes in this example are considered edge nodes (i.e., each node has its own traffic). In addition, node 1 and node 2 also play the role of core nodes (i.e., they can route traffic of the other nodes). In the optimal solution presented here (obtained by the resolution of the ILP model in Section 2 using CPLEX 1.11 solver [15]), wavelength intervals = [,2], 1 = [3,5], 2 = [6,8] and 3 = [9,11] are allocated to nodes 1, 3, and 2, respectively. Topology Wavelengths Intervals 1 2 3 3 1 2 3 Fig. 1. An example of wavelength partitioning using OTWP scheme. 6 9 11 The distance between the wavelength interval of node 1 and the wavelength interval of its neighbor, node 2, is D(,3) = 3. Similarly, for nodes and 1 we have D(2,) = 2 and for nodes 2 and 3 D(3,1) = 2. These distances could be calculated for each pair of nodes in the network. We can expect that whenever these distances increase, wavelength contentions are less likely to occur, especially, when corresponding nodes are sending bursts on overlapping paths. For example, consider the case where node 1 and node 2 are sending bursts to node 3; if node 1 searches for an available wavelength first in its wavelength interval (i.e., wavelengths [,2]) and node 2 searches for an available wavelength in its wavelength interval (i.e., wavelengths [9,11]), then wavelength contentions will occur less frequently than the case where both node 1 and node 2 search for available wavelengths using a classical approach, i.e., both nodes search for available wavelengths starting from wavelengths, 1, 2 and so on. Details on how the concept of distances between wavelength intervals is used practically are provided in Section 4. 3.2. Exact formulation We formulate the above wavelength partitioning problem as a combinatorial optimization problem; in the following we present the model formulation. Given: D½D i j Š Matrix of distances between wavelength intervals where D i j is calculated using Eq. (2). d[d ij ] Matrix of distances between nodes in the network where d ij = d ji is the number of hops of the shortest path between node i and node j. N The number of nodes in the network and the number of wavelength intervals (each one of size W/N); we have one wavelength interval per node. Variables: x ii Objective: Maximize Subject to: X N 1 i¼ X N 1 i ¼ A binary variable which takes the value 1 if wavelength interval i is allocated to node i; otherwise. C ¼ XN 1 X N 1 X N 1 X N 1 i¼ j¼iþ1 i ¼ j ¼ D i j d ij x ii x jj : ð3þ x ii ¼ 1 i ¼ ;...; N 1: ð4þ x ii ¼ 1 i ¼ ;...; N 1: ð5þ Bounds: x ii ¼ ; 1 i ¼ ;...; N 1 i ¼ ;...; N 1: The objective function (3) maximizes the sum of ratios [distance between wavelength intervals/distance between nodes] over all the possible solutions of the partitioning

3268 A. Belbekkouche et al. / Computer Networks 54 (21) 3264 3279 problem. Indeed, we can consider C as a metric that measures the quality of any solution. The rational behind using the ratio R ij ¼ D i j (for each pair of nodes i and j where i < j d ij and their allocated wavelength intervals i and j, respectively) is that we have a maximization problem where we aim to increase the distance D i j whenever the distance d ij is small. For example, let us consider again the topology shown in Fig. 1, the metric C = R 1 + R 2 + R 3 + R 12 + R 13 + R 23 is equal to 2 þ 1 þ 1 þ 3 þ 1 þ 2 in the optimal solution. We can see clearly that closer nodes have been allo- 1 2 3 1 2 1 cated distant wavelength intervals and vice versa, which is our aim. Furthermore, any other solution that does not respect this property will not be optimal. Constraint (4) states that each wavelength interval i is allocated to exactly one node i in the network. Constraint (5) states that each node i in the network has exactly one allocated wavelength interval i. This model is similar to the Quadratic Assignment Problem (QAP) [16] with the exception that we maximize the metric C instead of minimizing a cost in a typical QAP. In fact, a standard formulation of QAP is given by: Minimize p2s n X n i¼1 X n j¼1 a pðiþpðjþ b ij ; where S n is the set of permutations of {1,2,...,n} and each individual product a p(i)p(j) b ij is the cost caused by assigning facility p(i) to location i and facility p(j) to location j. Since the quadratic form in the objective function (3) makes the task of finding efficient resolution methods difficult, we formulate the problem as an Integer Linear Programming (ILP) model to benefit from its efficient resolution methods; thus, we define new variables y i j ij and a constraint (7) with new bounds. y i j ij ð6þ A binary variable which takes the value 1 if wavelength interval i is allocated to node i and wavelength interval j is allocated to node j; otherwise. 2y i j ij 6 x ii þ x jj ; ð7þ with bounds: y i j ij ¼ ; 1 i ¼ ;...; N 1 j ¼ i þ 1;...; N 1 i ¼ ;...; N 1 j ¼ ;...; N 1: Constraint (7) forces variables y i j ij to take the value 1 if both variables x ii and x jj take the value 1; this is always true because the coefficient of y i j ij, in the new objective function (8), is strictly positive in a maximization problem; otherwise, y i j ij takes the value. The new objective function becomes: in [17] proved that QAP is NP-hard. This difficulty to resolve QAPs can be seen in their computational complexity. In our case, we can see that the set of feasible solutions is the set of all possible permutations of {,...,N 1} which is n!. Indeed, to have a good idea of the computational complexity of our ILP, we tried to resolve it using CPLEX 1.11 solver. Whereas the resolution time is reasonable for small instances, such as the network shown in Fig. 1, it takes several days without returning the optimal solution for medium and large instances, such as 14-nodes NSFNET topology (Fig. 2). Hence, a meta-heuristic approach that returns good solutions (rather than the optimal solution) in a reasonable time is clearly mandatory in this case. 3.4. Tabu search algorithm The proposed tabu search algorithm aims to find, efficiently, a good solution to the wavelength partitioning problem in a reasonable time. Tabu search has been proposed by Glover in 1986 [18]. This meta-heuristic searches the best feasible solution starting from the neighborhood of an initial solution. The process is repeated until a maximum number of iterations is reached. Tabu search avoids cycles by forbidding moves that take the current solution to a solution previously visited. In our case, these moves represent tabu pair exchanges between the nodes in the network; they are stored in a list called tabu list. Let us define L as the function that returns the wavelength interval allocated to a given node; for instance, if wavelength interval i is allocated to node i, then L(i)=i. Also, let us denote a solution to the wavelength partitioning problem by a permutation P and the cost of this solution, defined in (8), by C(P). In our tabu search algorithm, a move represents an exchange of the assigned wavelength intervals between two nodes i and j, which means that if the current solution is a permutation P 1, then a new permutation P 2 is obtained by exchanging L(i) and L(j). The improvement when going from P 1 to P 2, denoted by D (P 1,P 2 ), is given by: DðP 1 ; P 2 Þ¼ XN 1 X N 1 k¼ h¼kþ1 D P 2 LðkÞLðhÞ d kh XN 1 X N 1 k¼ h¼kþ1 D P 1 LðkÞLðhÞ d kh ; ð9þ Maximize C ¼ XN 1 X N 1 X N 1 X N 1 i¼ j¼iþ1 i ¼ j ¼ D i j d ij y i j ij ð8þ 3.3. Complexity analysis Even formulated as an ILP, our model remains a Quadratic Assignment Problem (QAP). It is known that QAPs are not only NP-hard but also remain among the hardest combinatorial optimization problems. In fact, the authors Fig. 2. 14-nodes NSFNET topology.

A. Belbekkouche et al. / Computer Networks 54 (21) 3264 3279 3269 where D P 2 and D P 1 are the matrices of distances between wavelength intervals of solutions P 1 and P 2, respectively. The complexity of formula (9) is Oðn 2 Þ. We reduce this complexity to OðnÞ by rewriting (9) as follows: Lemma 1 DðP 1 ; P 2 Þ¼ XN 1 D P 2 LðkÞLðiÞ DP 1 1 d ki k¼ k i;j 1 d kj : ð1þ Proof. Without loss of generality, we suppose that we have always j > i. For each node k =,...,N 1, k i,j, we distinguish three cases: (1) k < i; (2) i < k < j; and (3) k > j. For the three cases, we define D 1 (P 1,P 2 ), D 2 (P 1,P 2 ) and D 3 (P 1,P 2 ), respectively, as follows: DðP 1 ; P 2 Þ¼D 1 ðp 1 ; P 2 ÞþD 2 ðp 1 ; P 2 ÞþD 3 ðp 1 ; P 2 Þ; where D 1 ðp 1 ; P 2 Þ¼ Xi 1 k¼ D 2 ðp 1 ; P 2 Þ¼ Xj 1 k¼iþ1 D 3 ðp 1 ; P 2 Þ¼ XN 1 k¼jþ1 k¼ k i;j D P 2 LðkÞLðiÞ d ki D P 2 LðiÞLðkÞ d ik D P 2 LðiÞLðkÞ d ik þ D P 2 d kj þ D P 2 þ D P 2 d kj LðjÞLðkÞ d jk D P 1 LðkÞLðiÞ d ki D P 1 D P 1 LðiÞLðkÞ d ik LðiÞLðkÞ d ik ð11þ D P 1! ; ð12þ d kj D P 1! ; ð13þ d kj D P 1! LðjÞLðkÞ : ð14þ d jk Since matrices D P 1 ; D P 2 and d are symmetric, we determine using (11) (14) that: DðP 1 ; P 2 Þ¼ XN 1 D P 2 LðkÞLðiÞ þ D P 2 D P 1 LðkÞLðiÞ D P 1! d ki d kj d ki d kj ¼ XN 1 k¼ k i;j k¼ k i;j D P 2 LðkÞLðiÞ DP 1 d ki ¼ XN 1 D P 2 LðkÞLðiÞ DP 1 1 d ki þ D P 2! LðkÞLðiÞ DP 1 d kj þ 1 d kj : ð15þ Table 1 shows the pseudo code of the proposed tabu search algorithm. The algorithm begins by the initialization step where an initial feasible solution has to be found. This can be performed by generating a random feasible solution which can be a very bad solution. Hence, to improve the efficiency of the proposed tabu search algorithm, we propose a simple heuristic algorithm, which is a Construction Method (CM), to compute an initial feasible solution. Table 2 shows the pseudo code of the proposed CM. CM uses a loop of N iterations (the number of nodes and wavelength intervals) where, at each iteration, a new node i is assigned a wavelength interval i that maximizes the metric: C ¼ X j2s D i LðjÞ d ij ; ð16þ Table 1 The Tabu Search algorithm (TS). Begin Step : Initialization Compute an initial feasible solution, denoted by P, using a construction method heuristic (see Table 2 for more details) best_cost = C(P ) int k = Step 1: loop while (k < Max_Iterations) Find in the set of neighbors {P m obtained using a non-tabu pair exchange on P k } of the current solution P k, the best solution P k+1 such that: DðP k ; P kþ1 Þ¼Max DðP k; P m mþ add the pair exchanged, to move from P k to P k+1, to the tabu list. If (C(P k+1 ) > best-cost) then best_cost = C(P k+1 ) k=k+1 End while End where S is the set of nodes which have already been assigned a wavelength interval. After that, in step1, at each iteration k between and Max_Iterations, the tabu search algorithm finds the best solution P k+1 in the neighborhood of the current solution P k using a non-tabu pair exchange; if the cost of solution P k+1 is better than the best-cost found until now (denoted by best_cost), best_cost will take the value of the cost of P k+1. The computational complexity of the loop in this algorithm is Oðn 2 Þ. The tabu list in our algorithm contains pairs (i,j) that cannot be exchanged in order to prevent cycles. We use a variable size tabu list, i.e., the size of the tabu list changes at each iteration of the algorithm. This approach improves the efficiency of the tabu search algorithm. Also, we implement this list as a two dimensional array which is updated in O(1). 4. Absolute fair Qos differentiation scheme In this Section, we present the proposed Absolute Fair Quality of service Differentiation scheme (AFQD). First, Table 2 The Construction Method heuristic (CM). Initialization S ={} S ¼fVg Var i, i, j Begin Find the node i with the highest degree in the network; S ={i } S ¼ S fi g L(i )= while ðs Þ do { i = the index of the node in S with the highest degree and which is a neighbor to one or more nodes in S L(i) =i such that P D i LðjÞ j2s is maximal. d ij S = S [ {i} } End S ¼ S fig

327 A. Belbekkouche et al. / Computer Networks 54 (21) 3264 3279 we describe the operation of AFQD. Then, we present the proposed wavelength assignment scheme for best effort traffic (BETWA). Finally, we present a solution for the starvation problem of low priority traffic. 4.1. The operation of AFQD AFQD uses the wavelength partitioning scheme OTWP, presented in Section 3, to provide absolute QoS differentiation. We assume that each wavelength interval assigned by OTWP to each edge node contains at least one wavelength. This assumption is very realistic since DWDM fiber links operate with tens to hundreds of wavelengths. Without loss of generality, we suppose that we have two classes of traffic: (a) Loss Sensitive (LS) traffic (e.g., mission critical applications traffic); and (b) Best Effort (BE) traffic. For simplicity, a burst belonging to LS traffic is called LS burst and a burst belonging to BE traffic is called BE burst. LS bursts have higher priority compared to BE bursts. We suppose that each OBS edge node has a burst assembly buffer for each destination OBS node and each class of traffic (i.e., LS or BE). Hence, an incoming packet from the client network (e.g., an IP network) is classified as LS or BE and forwarded to the appropriate assembly buffer according to: (1) its destination; and (2) its QoS requirements. After the burst assembly phase, each LS burst is transmitted using one of the wavelengths of its source node s wavelength interval (we call these wavelengths: local wavelengths) along the OBS network with loss-free transmission guarantee. Thus, LS bursts from a given source node will never contend with LS bursts of the other nodes, and naturally, will never contend among themselves since they are transmitted from the same source of traffic. Consequently, there will be no wavelength contentions, and hence, no LS burst losses inside the network. Moreover, any classical wavelength assignment policy can be used to assign a local wavelength to a LS burst in the source node (e.g., First-Fit or Random). Differently from LS bursts, BE bursts can use any wavelength at the OBS source node; consequently, BE bursts can contend with LS bursts and BE bursts of the other nodes in the network. Let us note that wavelength assignment at the OBS source node is decisive because of the absence of wavelength converters at the OBS core nodes. Thus, bursts (LS and BE) will use the same wavelength up to their OBS destination nodes. When two BE bursts are involved in a wavelength contention, one of the two bursts is dropped randomly; when a LS burst and a BE burst are involved in a wavelength contention, the LS burst is privileged to maintain the loss-free transmission guarantee; hence, even if a BE burst has already performed wavelength reservation, a LS burst can cancel this reservation and preempt the BE burst. If a LS burst cannot reserve a wavelength (in its OBS source node) even by preempting a BE burst, this will mean that the local wavelengths of this node are fully used by LS bursts; in this case, the LS burst can be stored (in the electronic domain) until a local wavelength becomes available, or it can be simply dropped. This can be seen as an admission control mechanism for LS traffic; a LS burst will never contend with another LS burst once it reserves a wavelength at its OBS source node. Fig. 3 shows the operation of AFQD to schedule a LS burst at OBS source node. The test of LS traffic local wavelengths bandwidth utilization (and threshold U) is related to the starvation problem which is discussed in subsection 4.3. So far, we have explained how to guarantee loss-free transmission for LS bursts; the remaining challenge is to improve the performance of BE traffic as much as possible. For that, we propose a novel wavelength assignment scheme, called Best Effort Traffic Wavelength Assignment scheme (BETWA), to improve the performance of BE traffic. 4.2. Best effort traffic wavelength assignment scheme BETWA is a general wavelength assignment scheme that can be used also in the classless case. However, we call it so to highlight its role in the scope of this paper (i.e., absolute QoS differentiation). BETWA uses OTWP wavelength partitioning solution to find an available wavelength to transmit Best Effort (BE) bursts. Indeed, given a solution to the wavelength partitioning problem returned by OTWP, in a node i, BETWA searches an available wavelength to transmit a BE burst starting from the start wavelength of wavelength interval (i + 1); the search process starts from wavelength interval (i + 1) to alleviate contentions among LS bursts and BE bursts originating from the same node; also, since the closer the nodes to node i (e.g., one hop neighbors) the distant their wavelength intervals to i, wavelength contentions (and hence burst losses) among BE bursts will be considerably decreased. It is worth noting that a source node can assign any available wavelength (from the set of all wavelengths) to a BE burst; however, the order in which this available wavelength is searched is specific. Indeed, for a source node i with wavelength interval i, BETWA searches an available wavelength as follows: (1) starting from start wavelength of wavelength interval (i + 1) to last wavelength of wavelength interval N; (2) from the last wavelength of wavelength interval (i 1) to the start wavelength of wavelength interval (in the reverse direction); and finally (3) in the wavelength interval i (from start wavelength to last wavelength). This order is adopted to benefit from the concept of distance between intervals. We conclude that OTWP maximizes (implicitly) the traffic isolation between the different nodes in the network. For example, in Fig. 1, if BETWA is not used and a classical wavelength assignment is used instead (e.g., First-Fit), BE bursts originating from nodes 1 and 2 with destination are more likely to contend on the link from node 1 to node. Fig. 4 shows the order in which BETWA searches an available wavelength to schedule a BE burst at node i with wavelength interval i. Fig. 5 shows the operation of AFQD to schedule a BE burst at an OBS source node. 4.3. Starvation problem for BE traffic Since LS bursts have the ability to preempt BE bursts, the BE bursts could suffer from the starvation problem when LS bursts use all of the available bandwidth in the network (i.e., each node uses fully its local wavelengths for LS traffic). Moreover, since the OBS network is considered, generally, as a transport network that serves client

A. Belbekkouche et al. / Computer Networks 54 (21) 3264 3279 3271 Source Node Schedule a LS burst to be transmitted at source node Find an available local wavelength No Available local wavelength found Yes No LS traffic bandwidth utilization on local wavelengths < U Yes Find a BE burst to preempt No BE burst found Yes Drop the burst Reserve the wavelength to transmit the burst Exit scheduling Fig. 3. The operation of AFQD to schedule a LS burst at source node. networks (e.g., IP networks, ATM networks, etc.), it is not always possible to predict the amount of LS traffic while planning the OBS network. Hence, allowing unrestricted preemption of BE bursts makes it impossible to solve the problem of starvation. We propose to disable the preemption of BE bursts at an outgoing fiber link of a source node when the bandwidth utilization of LS traffic exceeds a predefined threshold, denoted by U, of the local wavelengths bandwidth of this node on this outgoing link (e.g., 8%). Thus, each OBS edge node has to monitor the bandwidth utilization of LS traffic at each one of its outgoing fiber links; whenever this bandwidth utilization exceeds the threshold U on a given outgoing fiber link, LS bursts cannot preempt BE bursts that have already reserved resources on this link. In this case, LS bursts are stored (in the electronic domain) until resources become available or simply dropped at the source node (admission control); this still preserves the loss-free transmission guarantee for LS traffic inside the OBS network. This scheme is simple since it operates only in the OBS edge nodes. Also, it allows LS traffic to use the whole capacity of the node s local wavelengths on a link when no (or negligible) BE traffic uses this link. 5. Wavelength borrowing protocol So far, we have assumed that each OBS edge node has the same number of local wavelengths to send its LS traffic. Source Node No Schedule a BE burst to be transmitted at source node Use BETWA to find an available wavelength Available wavelength found Yes Drop the burst Reserve the wavelength to transmit the burst Exit scheduling Fig. 4. The order in which BETWA searches an available wavelength at node i with wavelength interval i. Fig. 5. The operation of AFQD to schedule a BE burst at source node.

3272 A. Belbekkouche et al. / Computer Networks 54 (21) 3264 3279 However, an unbalanced (non-uniform) LS traffic in the network (i.e., some OBS edge nodes need to send more LS traffic than the capacity of their local wavelengths while other OBS edge nodes have no (or negligible) amount of LS traffic to send) may result in decreasing the performance of AFQD and thus degrading bandwidth utilization. To tackle this problem, we propose a wavelength borrowing scheme, called Wavelength Borrowing Protocol (WBP), which operates as follows: each OBS edge node keeps track of the amount of LS traffic sent on each one of its outgoing fiber links; whenever this amount exceeds the capacity of local wavelengths on an outgoing link, the node broadcasts a BORROW packet to the other edge nodes in the OBS network to request the use of a specific number of available unused wavelengths (depending on the amount of exceeding LS traffic) among the local wavelengths of other edge nodes. Each edge node receiving a BORROW packet checks the utilization of its local wavelengths and answers this request only if it has available (non-utilized) wavelength (s); this is performed by reserving the available wavelengths (up to the requested number of wavelengths) and by sending a RESPONSE packet directly to the requesting node. If the node can provide the total number of requested wavelengths, it does not broadcast the received BORROW packet; however, if (a) it can only borrow a subset of the requested wavelengths; or (b) it cannot borrow any wavelength, it broadcasts the received BORROW packet to its neighbors. Each OBS edge node keeps track of the identifiers of the received BORROW packets to eliminate duplicates (i.e., when a BORROW packet is received twice or more). A requesting node can borrow from several nodes for the same request if none of the responding nodes can provide its requested number of wavelengths. Upon receipt of RESPONSE packet, a requesting node responds the borrowing node by an ACCEPT packet if it accepts all or a subset of the proposed wavelengths; otherwise it sends a RELEASE packet to release all of the reserved wavelengths. The requesting node sends a RELEASE packet only if its demand in terms of wavelengths has been fulfilled by other nodes in the network. Upon receipt of AC- CEPT packet, the borrowing node keeps the reservation of wavelengths included in the ACCEPT packet and makes available the wavelengths that were sent in RESPONSE packet and not included in ACCEPT packet. For better understanding, let us consider the following example: node1 sends BORROW packet requesting 3 wavelengths; node2, node3 and node4 send 3 RESPONSE packets including (wavelength1, wavelength2), (wavelength3, wavelength4), and (wavelength5, wavelength6), respectively. Node1 sends 2 ACCEPT packets including (wavelength1, wavelength2) and (wavelength3) to node2 and node3, respectively; it also sends RELEASE packet to node4. Node3 and node4 will make available wavelength4 and (wavelength5, wavelength6), respectively. To ensure the stability of the wavelengths borrowing scheme and alleviate fluctuations, especially at the beginning of the network operation and when the traffic pattern is not yet in stable state (i.e., when the traffic pattern changes in very short time scale), WBP uses a timer to trigger any wavelength borrowing process; i.e., whenever LS traffic exceeds the capacity of local wavelengths on an outgoing link of a node, this node should wait a period of time T BORROW, during which its LS traffic amount does not decrease under local wavelengths capacity, before sending a BORROW packet. Similarly, a borrowing node should wait a period of time T BORROW during which its LS traffic amount does not increase above local wavelengths capacity, before sending a RESPONSE packet. Parameter T BORROW can be set by the network operator. When a borrowing node needs to recover its borrowed wavelengths (after an increase of its LS traffic), it sends a RECOVER packet to each node for which it has borrowed wavelengths. This node has to answer by a RELEASE packet to confirm that the borrowing node may again use its local wavelength (s). Fig. 6 shows the fields of WBP packets: ID: the identifier of the packet; Packet type: determines whether the packet is BORROW, RESPONSE, ACCEPT, RELEASE or RECOVER; Source address: the node that sends the packet; Destination address: the destination node of the packet; if this is a BORROW packet, the value of this field is a broadcasting address; Number of wavelengths: the number of wavelengths: (a) that are requested if the packet is BORROW; (b) that can be borrowed if the packet is RESPONSE; (c) that are actually borrowed if the packet is ACCEPT; and (d) that the borrowing node request to recover if the packet is RECOVER; List of wavelengths: used to determine the list of wavelengths that can be borrowed in a RESPONSE packet, the wavelengths actually borrowed in an ACCEPT packet and the list of wavelengths to recover in a RECOVER packet; TTL (Time-To-Live): used to prevent BORROW packets from being broadcasted indefinitely in the OBS network; the value of this field is decreased at each hop. An appropriate initial value of this filed should be equal to the diameter of the OBS network. Fig. 7 shows the interactions of WBP. Fig. 7(a) shows the interactions when a node requests wavelength (s) for its LS traffic and accepts all or a subset of the proposed wavelengths. Fig. 7(b) shows the interactions when a node requests wavelengths (s) and release all of the proposed wavelengths (if its request has been fulfilled by the other nodes). Fig. 7(c) shows the interactions when a borrowing node requests to recover its borrowed wavelengths (s). It is worthwhile to note that the control packets of WBP, namely, BORROW, RESPONSE, ACCEPT, RELEASE and RE- COVER will be sent on the control wavelength (s) of the OBS network. In addition, the fact that these packets have small sizes and the fact that they are sent sporadically (i.e., only when LS traffic on an outgoing link of a node exceeds ID Packet type Source address Destination address Number of wavelengths Fig. 6. The fields of WBP packets. List of wavelengths TTL

A. Belbekkouche et al. / Computer Networks 54 (21) 3264 3279 3273 Requesting node Borrowing node Requesting node Borrowing node BORROW BORROW RESPONSE RESPONSE ACCEPT RELEASE (a) Requesting node (b) Borrowing node RECOVER RELEASE (c) Fig. 7. WBP interactions. its local wavelengths capacity) make them less likely to congest the control plan of the OBS network. Also, let us note that the loss of a WBP control packet (e.g., RELEASE packet) will need the use of timers and retransmission to make WBP reliable (i.e., TCP-like approach [19]); however; this is out of the scope of this paper since we suppose that the medium is reliable and that there is no congestion in the control plan. 6. Numerical results In this Section, we present numerical results of CPLEX and Tabu Search algorithm and simulation results that show the performance of AFQD, WBP and BETWA. We use ns-2 simulator [2] and modules that implement OBS in ns-2 [21]. We consider three kinds of topologies: (1) mesh topologies represented by NSFNET with 14 nodes (Fig. 2); (2) regular topologies represented by 4 4 nodes regular torus topology (Fig. 8(a)); and (3) ring topologies represented by a 15-nodes ring topology (Fig. 8(b)). Let us notice that we consider ring topologies because they have a primordial importance in metro and access optical networks. We present NSFNET topology results in the majority of figures to alleviate presenting a huge number of figures, especially, when the general behavior is the same for all of the topologies. We assume that each single fiber link is bidirectional and all links have the same number of wavelengths. Each node in the network can generate, route and receive traffic (i.e., each node in the network is an edge and core node at the same time). Sources and destinations of traffic connections are generated randomly between any two nodes in the network, i.e., the traffic is dynamic and uniform; however, we use non-uniform traffic to measure the performance of WBP. The traffic load is expressed as the percentage of the total load that can be carried by the network (i.e., Traffic Load ¼ðOffered LoadÞ= ½ð P Link capacitiesþ=ðmean path size in the networkþš) where Offered Load is the amount of traffic injected, per second, in the network and the capacity of a link is the sum of the capacities of all the wavelengths in this link. We use Min Burst length Max Assembly Period (MBMAP) algorithm for burst assembly [22]. We use exponential ON/OFF traffic and shortest path for routing. We consider loss probability which is the main performance metric in buffer-less OBS networks. Also, if a LS burst cannot be scheduled at an OBS source node, it is simply dropped (and not stored); the corresponding client networks are notified. Hence, LS bursts will not undergo additional delay at the border of the OBS network. All the following results have a confidence level of 95%. 6.1. Results of CPLEX and tabu search To measure the quality of the proposed Tabu Search algorithm (TS) solutions, we performed experiments that compare the cost of its solutions to the cost of the solutions returned by CPLEX after a running time of 24 h (i.e., CPLEX has to return the solution, if any, at most after 24 h; this solution may be not optimal). Table 3 shows the average cost of solutions for random instances (topologies) of sizes from 1 to 1 nodes. We can see that CPLEX is unable to find solutions for instances of 5 nodes and more; this is because CPLEX needs an unrealistic amount of memory space to find even a first feasible solution for these instances. Moreover, these numerical results show that TS algorithm returns better solutions compared to CPLEX in few seconds to few minutes. Indeed, TS improves the solutions of CPLEX by.51% to 4.3% for instances between 1 nodes and 4 nodes. From computational time point of view, TS finds its solutions in less than 1 s for 1 nodes and 1576.5 s for 1 nodes.

3274 A. Belbekkouche et al. / Computer Networks 54 (21) 3264 3279 (a) (b) Fig. 8. (a) 4 4 regular topology and (b) 15-nodes ring topology. the objective of using BETWA is to improve the performance of BE traffic when AFQD is offering absolute QoS provisioning to LS traffic. Simulation results of BETWA in the classless case (without QoS provisioning) are presented in subsection 6.3. We present: (a) AFQD: the overall loss probability for all of the bursts (i.e., blocking probability for LS bursts and loss probability for BE bursts); (b) LS: the blocking probability for LS traffic at the access of the OBS network (admission control blocking probability) since the loss probability of LS traffic is equal to zero inside the OBS network; and (c) BE: the loss probability for BE traffic. Also, to give an idea about the improvement brought by AFQD to the performance of OBS network, we plot the performance results of Latest Available Unscheduled Channel with Void Filling (LAUC-VF) [23] which is a good wavelength assignment algorithm that outperforms largely the classical wavelength assignment policies (e.g., First-Fit and Random). We note that since AFQD guarantees loss-free transmission to high priority traffic, it is not appropriate to compare it to existing QoS schemes for OBS networks which, in general, assume a maximum loss threshold for high priority traffic. We fix the value of the threshold U to.8, i.e., preemption is disabled when the bandwidth utilization of LS traffic reaches 8% of the bandwidth capacity of the local wavelengths of a node on an outgoing link. Unless stated otherwise, the amount of LS traffic that each node injects in the network is 1/N of the overall traffic that the node injects in the network (1/ N represents the ratio [number of local wavelengths of each node (W/N)/total number of wavelengths in each fiber link (W)]). The remaining amount (i.e., [1-(1/N)]) is BE traffic. Fig. 9 shows the performance of AFQD compared to LAUC-VF. We can see that AFQD reduces effectively the loss probability of the OBS network. Indeed, whereas the mean loss probability of LAUC-VF (over all of the loads) is about.46, the mean loss probability of AFQD is about.29. In addition, whereas at load 5% loss probability of LAUC-VF is.47, it is.26 for AFQD. This proves that AFQD is not only able to provide absolute QoS differentiation for Table 3 Comparison of tabu search (TS) and CPLEX results. Nodes CPLEX TS 1 129.16 129.83 2 759 783.8 3 2191.92 2261.78 4 4955.67 5177.92 5 862.8 6 15,216.1 7 22,185 8 3,174 9 37,827.2 1 38,726.5.7.6.5.4.3.2.1 AFQD LAUC-VF 6.2. Results of AFQD The goal of these simulations is to measure the performance of AFQD. Since BETWA is a component of AFQD, we use it as a wavelength assignment scheme for BE traffic; 1 2 3 4 5 6 7 8 9 1 Fig. 9. Loss probability vs. load for AFQD and LAUC-VF on NSFNET with 64 wavelengths.

A. Belbekkouche et al. / Computer Networks 54 (21) 3264 3279 3275 Blocking Probability 1 1-1 1-2 1-3 LS (.5(1/N)) LS (1/N) LS (2(1/N)) 1-4 2 3 4 5 6 7 8 9 1 Fig. 11. LS traffic blocking probability on NSFNET with 64 wavelengths. the OBS network, but also it can reduce its loss probability to a remarkable level for the network under study (i.e., without wavelength converters and FDLs). The same behavior is observed for regular and ring topologies (related figures are not presented here). Fig. 1 shows the loss probability for BE traffic when varying the proportion of LS traffic (of the overall traffic in the network) from.5(1/n) to 2(1/N). We can see clearly that the proposed wavelength assignment scheme for BE traffic (BETWA) is efficient in reducing loss probability of BE traffic regardless of its proportion. Indeed, we can see that even at load 5%, the loss probability for BE traffic is in the order of.2. Also, we can see that BE loss probability slightly increases when the proportion of LS traffic increases which was expected. Fig. 11 shows the blocking probability of LS traffic at the source OBS edge nodes when varying the proportion of LS traffic. This blocking could happen when the LS traffic bandwidth utilization of the local wavelengths of a node on an outgoing link exceeds the threshold U (8% in these simulations). We can see that this blocking probability is at most in the order of 1 2 when the proportion of LS traffic is (1/N) (i.e., LS traffic uses 1% of local wavelengths bandwidth capacity); this is comparable to the high priority traffic loss target in other QoS schemes (e.g., 1 2 in [9] and 2 1 3 in [1]) where losses are allowed inside the OBS network. Also, we can see that this blocking probability increases when the proportion of LS traffic increases; for example, when the proportion of LS traffic is 2(1/N) (i.e., twice the capacity of local wavelengths), LS bursts blocking probability may reach 1 1 at load 5%. From Figs. 1 and 11 we observe that blocking probability of LS traffic is significantly lower than the loss probability of BE traffic. This proves that AFQD successfully provides QoS differentiation among LS traffic and BE traffic. Fig. 12 shows loss probability of AFQD and LAUC-VF when varying the number of wavelengths from 32 to 16 using NSFNET topology and fixing the traffic load at 5% of the capacity of the network at each value of the number of wavelengths (obviously, the amount of traffic corresponding to 5% traffic load increases when the number of wavelengths increases). We can see that whatever the number of wavelengths, AFQD outperforms significantly LAUC-VF. Also, we observe that whereas loss probability of LAUC-VF increases when the number of wavelengths increases, loss probability of AFQD slightly decreases. Indeed; this behavior was expected since the size of each wavelength interval (the number of local wavelengths) in OTWP becomes larger when the number of wavelengths increases; this increases the capability of traffic isolation amongst the nodes in the OBS network. Also, this proves that AFQD is more efficient when using DWDM technology where each fiber link operates with a large number of wavelengths. Furthermore, the increase of loss probability of LAUC-VF when increasing the number of wavelengths is explained by the fact that LAUC-VF is unable to exploit the increase of the number of wavelengths; indeed, it performs wavelength assignment in each node using only local information and without considering the traffic of the other nodes in the network..7.6 BE (.5(1/N)) BE (1/N) BE (2(1/N)).5 AFQD LAUC-VF.5.4.3.2.4.3.2.1.1 1 2 3 4 5 6 7 8 9 1 32 64 96 128 16 Number of Wavelengths Fig. 1. BE traffic loss probability vs. load on NSFNET with 64 wavelengths. Fig. 12. Loss probability of AFDQ and LAUC-VF on NSFNET when varying the number of wavelengths.

3276 A. Belbekkouche et al. / Computer Networks 54 (21) 3264 3279 Fig. 13 shows loss probability of BE and LAUC-VF and blocking probability of LS using 4 4 regular topology and 64 wavelengths. We can see that the trends are similar to the case of NSFNET topology. Fig. 14 shows loss probability of BE and LAUC-VF and blocking probability of LS using 15-nodes ring topology. Here again, the results are similar to those of NSFNET and regular topologies. In addition, we observe that LS blocking probability performance is better compared to NSFNET and regular topologies. In fact, the blocking probability of LS traffic is as low as 1 4 at 2% load. We conclude that AFQD performs better in OBS ring networks which are, usually, used for optical Metropolitan Area Networks (MANs). This proves that AFQD is able to provide QoS differentiation and reduce significantly loss probability regardless of the topology of the OBS network. 6.3. Results of BETWA As stated in subsection 4.2, BETWA can be seen as a separate contribution in the context of wavelength assignment for classless OBS networks. Thus, we perform simulations to measure the performance of BETWA in the general case (classless case). We compare BETWA to Latest Available Unscheduled Channel with Void Filling (LAUC-VF) [23] and Q-learning algorithm for Wavelength Selection (QWS) [14] (see Section 2). LAUC algorithm uses the latest available wavelength, i.e., the available wavelength with the minimum time interval between the end time of the last scheduled burst and the start time of the burst to be scheduled. Void Filling (VF) has been introduced to allow scheduling bursts in voids (i.e., between two already scheduled bursts) and hence, reduces fragmentation and increases wavelength utilization. The motivations behind comparing BETWA to LAUC-VF and QWS are: (a) LAUC-VF is a good wavelength assignment algorithm that outperforms largely the classical wavelength assignment policies (e.g., Loss / Blocking Probability 1 1-1 1-2 1-3 1-4 LS BE LAUC-VF 2 3 4 5 6 7 8 9 1 Fig. 14. Blocking probability of LS and Loss probability of BE and LAUC-VF on 15-nodes ring topology with 64 wavelengths. First-Fit and Random); and (b) QWS is a recent scheme for wavelength assignment in OBS networks that outperforms PWA-link and First-Fit-TE [12] (see Section 2); hence, by comparing BETWA to QWS, we are comparing it indirectly to PWA-link and First-Fit-TE. For QWS parameters, we use the same values reported in [14]. Fig. 15 shows loss probability with NSFNET topology and 64 wavelengths. We can see clearly that BETWA outperforms LAUC-VF and QWS. In fact, the mean burst loss probability (over all of the loads) of BETWA, QWS and LAUC-VF are.27,.53 and.46, respectively. We conclude that BETWA reduces effectively loss probability. Also, we observe that QWS is better than LAUC-VF only for low traffic loads (i.e., under 2%). To measure the impact of varying the number of wavelengths in each fiber link on the performance of BETWA, we consider NSFNET topology and vary the number of wavelengths from 32 to 16 while fixing the traffic load Loss / Blocking Probability 1 1-1 1-2 1-3.7.6.5.4.3.2 BETWA LAUC-VF QWS 1-4 LS BE LAUC-VF 1 2 3 4 5 6 7 8 9 1 Fig. 13. Blocking probability of LS and Loss probability of BE and LAUC-VF on 4 4 regular topology with 64 wavelengths..1 1 2 3 4 5 6 7 8 9 1 Fig. 15. BETWA: loss probability vs. load with NSFNET and 64 wavelengths.

A. Belbekkouche et al. / Computer Networks 54 (21) 3264 3279 3277.7.5.6.4.3.2.5.4.3.2.1 BETWA LAUC-VF QWS 32 64 96 128 16 Number of Wavelengths Fig. 16. BETWA: loss probability vs. number of wavelengths with NSFNET topology when load is fixed to 5%. BETWA.1 LAUC-VF QWS 1 2 3 4 5 6 7 8 9 1 Fig. 18. BETWA: loss probability vs. number of wavelengths with ring topology and 64 wavelengths. at 5% of the network capacity when varying the number of wavelengths (Fig. 16). We can see that, whatever the number of wavelengths, BETWA outperforms the other schemes. Also, we observe that whenever the number of wavelengths increases, the performance of BETWA becomes slightly better; this is because the size of wavelength intervals increases and because BETWA exploits efficiently the additional bandwidth offered by the increase of the number of wavelengths; this is not the case of (a) LAUC-VF which performs wavelength assignment based on local information in each node; and (b) QWS which performs wavelength assignment in each node by probing the state of the network using a reinforcement learning approach. With regular topology (Fig. 17) and 64 wavelengths, we observe the same trends as with NSFNET topology (Fig. 15). However, in ring topology (Fig. 18), QWS is better than LAUC-VF whatever the value of traffic load in the network. 6.4. Results of WBP To show the capability of WBP to reduce blocking probability of LS traffic, we perform simulations using non-uniform LS traffic where only half of the network nodes send LS traffic. We set the proportion of LS traffic to twice the capacity of local wavelengths in each sending node (i.e., 2(1/N)). Fig. 19 shows blocking probability of LS traffic with WBP and without WBP on NSFNET topology with 64 wavelengths. We can see clearly that WBP is able to reduce effectively blocking probability of LS traffic, especially, when the traffic pattern is non-uniform and when some nodes are not fully using their local wavelengths. Indeed, the mean blocking probability (over all of the loads) of LS traffic when using WBP is.7 and the mean blocking probability without using WBP is.32..7.6.5.4.3 BETWA LAUC-VF QWS 1 1-1 1-2.2 1-3.1 1 2 3 4 5 6 7 8 9 1 Fig. 17. BETWA: loss probability vs. number of wavelengths with 4 4 nodes regular topology and 64 wavelengths. 1-4 WBP without WBP 2 3 4 5 6 7 8 9 1 Fig. 19. Blocking probability of LS with and without WBP on NSFNET and 64 wavelengths.

3278 A. Belbekkouche et al. / Computer Networks 54 (21) 3264 3279 1 1-1 1-2 1-3 1 1-1 1-2 1-3 1-4 2 3 4 5 6 7 8 9 1 4 5 6 7 8 9 1 The same trends as NSFNET are observed for regular topology (Fig. 2); when WBP is used, it reduces effectively blocking probability when the LS traffic pattern is nonuniform. Fig. 21 shows the performance of WBP with ring topology. We observe that, in ring topology, WBP performs better compared to NSFNET and regular topologies. In fact, at 4% load, WBP is able to reduce LS traffic blocking probability by orders of magnitude, i.e., from 1 1 to 1 4. 7. Concluding remarks WBP without WBP Fig. 2. Blocking probability of LS with and without WBP on regular topology with 64 wavelengths. WBP without WBP Fig. 21. Blocking probability of LS with and without WBP on ring topology and 64 wavelengths. In this paper, we have proposed an absolute QoS differentiation scheme for OBS networks (AFQD). AFQD is based on a wavelength partitioning scheme (OTWP) which models the wavelength partitioning problem as an Integer Linear Programming (ILP) model and uses a tabu search algorithm to resolve it efficiently. AFQD guarantees lossfree transmission inside the OBS network for high priority traffic (Loss Sensitive (LS) traffic) whatever the kind of the OBS network topology. In addition, AFQD uses a novel wavelength assignment scheme (BETWA), based on OTWP, to improve the performance of Best Effort (BE) traffic in terms of loss probability. Also, BETWA can be used as an efficient wavelength assignment scheme in the context of classless OBS networks. To make AFQD adaptive to nonuniform traffic patterns, we proposed a wavelength borrowing protocol (WBP). Simulation results did show that: (1) AFQD is effective to provide absolute QoS differentiation and to guarantee loss-free transmission for LS traffic; (2) BETWA decreases, significantly, loss probability for BE traffic (with AFQD) and overall traffic (without AFQD) to a remarkably low level for the OBS network under study; (3) WBP is capable of reducing, effectively, blocking probability of LS traffic with non-uniform traffic. References [1] C. Qiao, M. Yoo, Optical burst switching (OBS) a new paradigm for an optical internet, Journal of High Speed Networks 8 (1) (1999) 69 84. [2] H. Guo, et al., A testbed for optical burst switching network, in: Proceedings of OFC/NFOEC 5, 25. [3] Y. Sun et al., Design and implementation of an optical burst-switched network testbed, IEEE Communications Magazine 43 (11) (25) S48 S55. [4] EtherBurst optical switch, <http://www.matissenetworks.com>. [5] M. Yoo, C. Qiao, S. Dixit, QoS performance of optical burst switching in IP-over-WDM networks, IEEE Journal on Selected Areas in Communications 1 (1) (2) 262 271. [6] Y. Chen, M. Hamdi, D.H.K. Tsang, Proportional QoS over OBS networks, in: Proceedings of IEEE GLOBECOM, 21. [7] S. Kim, J.S. Choi, M. Kang, Providing absolute differentiated services for optical burst switching networks: loss differentiation, IEE Proceedings-Communications 152 (4) (25) 439 446. [8] Q. Zhang et al., Absolute QoS differentiation in optical burstswitched networks, IEEE Journal on Selected Areas in Communications 22 (9) (24). [9] J. Phuritatkul, Y. Ji, S. Yamada, Proactive wavelength preemption for supporting absolute QoS in optical burst-switched networks, Journal of Lightwave Technology 25 (5) (27). [1] Lui Hongbo, H.T. Mouftah, A new absolute QoS differentiation scheme supporting best-effort class in OBS Networks, in: Proceedings of ICTON 7, 27. [11] Lui Hongbo, H.T. Mouftah, Absolute QoS differentiation with besteffort class support in optical burst switching networks, in: Proceedings of ISCC 7, 27. [12] J. Teng, G.N. Rouskas, On wavelength assignment in optical burst switched networks, in: Proceedings of BROADNETS 4, 24. [13] X. Wang, H. Morikawa, T. Aoyama, Priority-based wavelength assignment algorithm for burst switched WDM optical networks, IEICE Transactions on Communications E86-B (5) (23) 158 1514. [14] Y.V. Kiran, T. Venkatesh, C.S.R. Murthy, A reinforcement learning framework for path selection and wavelength selection in optical burst switched networks, IEEE Journal on Selected Areas in Communications 25 (9) (27) 18 26. [15] ILOG CPLEX 1., <http://www.ilog.com>. [16] P.M. Pardalos, F. Rendl, H. Wolkowicz, The quadratic assignment problem: a survey and recent developments, in: Proceedings of the DIMACS Workshop on Quadratic Assignment Problems, 1994. [17] S. Sahni, T. Gonzalez, P-complete approximation problems, Journal of the Association of Computing Machinery 23 (1976) 555 565. [18] F. Glover, Future paths for integer programming and links to artificial intelligence, Computers and Operations Research 5 (1986) 533 549. [19] W. Stallings, Data and Computer Communications, Prentice Hall, 26. [2] NS-Simulator, <http://www.isi.edu/nsnam/ns>. [21] S. Gowda, et al., Performance evaluation of TCP over optical burstswitched (OBS) WDM networks, in: Proceedings of IEEE ICC, 23. [22] X. Cao, et al., Assembling TCP/IP packets in optical burst switched networks, in: Proceedings of IEEE GLOBECOM, 22.

A. Belbekkouche et al. / Computer Networks 54 (21) 3264 3279 3279 [23] Y. Xiong, M. Vandenhoute, H.C. Cankaya, Control architecture in optical burst-switched WDM networks, IEEE Journal on Selected Areas in Communications 18 (1) (2) 1838 1851. Abdeltouab Belbekkouche is currently a Ph.D. candidate at Université de Montréal (Canada). He received his Master s degree from Université d Orléans (France) and Engineer s Diploma in Computer Engineering from Univesité d Oran (Algeria). He is a member of the Network Research Lab (NRL) of the University of Montreal and the Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation (CIRRELT). His current research interests include optical networks design and management, wireless and optical networks integration, learning and optimization techniques, switching paradigms, quality of service and congestion control. Abdelhakim Hafid is Professor at département d Informatique et de recherche opérationnelle de l Université de Montréal, where he founded the Network Research Lab (NRL) in 25. Prior to joining University of Montreal, he was with Telcordia Technologies (formerly Bell Communication Research), NJ, US, faculty at University of Western Ontario, research director at Advance Communication Engineering Center, Canada, researcher at Computer Research Institute of Montreal, Canada, and visiting scientist at GMD-Fokus, Germany. He has extensive academic and industrial research experience in the area of the management of next generation networks including wireless and optical networks, QoS management, distributed multimedia systems, and communication protocols. Mariam Tagmouti received an M.S degree in applied mathematics in Mohammadia Engineering School, Rabat, Morocco and a Ph.D. in Computer Science and Operational research in the University of Montréal in 28. Her doctoral research focused on vehicle and arc routing problems with time dependent service costs. In 29 she did a postdoctoral fellowship at the Network research Lab (NRL) in the University of Montréal where she collaborated with graduated students to realize many works on wavelength assignment problems in OBS Networks and designing cellular networks. Now, she is working in industry in R&D projects. Her research interests are: Transportation problems, dynamic problems, combinatorial optimization, heuristics and exact methods to solve problems in logistics, transportation and telecommunications. Michel Gendreau is Professor of Operations Research at the Department of Applied Mathematics and Industrial Engineering of École Polytechnique de Montréal (Canada). He received his Ph.D. from University of Montreal in 1984. From 1999 to 27, he was the Director of the Centre for Research on Transportation, a centre devoted to multi-disciplinary research on transportation and telecommunications networks. His main research interests deal with the development of exact and approximate optimization methods for transportation and telecommunications network planning problems. He has worked for more than 2 years on telecommunication network design and dimensioning problems, with a focus on the development of specialized optimization algorithms for these classes of problems.